Name: ___________________________________ Date: _________________________
Period:_____
5-1 – 5-4 Review
Write each polynomial in standard form. Then classify it by degree and by number of terms.
Simplify first.
1. 6  2x3  4 + x3
2. (4s4  s2  3)  (3s  s2  5)
3. b(b  3)2
Write a polynomial function in standard form with the given zeros.
4. x = 2, 1, 4
5. x = 3, 8, 0
6. x = 4, 1
Find the zeros of each function. State the multiplicity of multiple zeros. (Factor first)
7. y = (x  3)2(x + 1)
8. y = x3 + 11x2 + 30x
9. y = 2x2  2x
10. x3  3x2  x + 3
11. 9x3  81x
12. y = x4  8x3 + 16x2
14. x4  x =0
15. x4  81 = 0
Solve each equation.
13. 2x4  26x2  28 = 0
Name: ___________________________________ Date: _________________________
Period:_____
Divide using long division. Check your answers.
16. (2x2 + x  7) ÷ (x  5)
17. (3x3  x2  7x + 6) ÷ (x + 2)
Divide using synthetic division.
18. (2x3 + 15x2  22x  15) ÷ (x  3)
19. (2x4 + 7x3  11x2 + 21x + 5) ÷ (x + 5)
Use synthetic division and the given factor to completely factor the polynomial function.
20. y = x3 + 3x2  13x  15; (x + 5)
Use synthetic division and the Remainder Theorem to find P(a).
21. P(x) = x3 + 7x2 + 12x  3; a = 5. Find P(-5)
22. Reasoning What does it mean if P(4) for the polynomial function P(x) = x3 + 11x2 + 34x + 24 equals
zero?